A brief study of instabilities in the context of space magnetohydrodynamic simulations

Abstract

The study of the hydrodynamic instabilities in the context of the magnetohydrodynamics (MHD) is very important in many branches of physics. Particularly, we can mention geophysical and astrophysics, where we have several processes involving hydrodynamic effects, such as shock waves, plasma flows and the propagation of waves. In these scenarios it is frequent the onset of instabilities. For example, let a system be formed by two phases with different densities and relative velocities. Besides, consider these phases are in contact with each other by means of a tangential surface, that is, an interface where there is no transference of matter and where there are only relative tangential velocities. In this case, under certain circumstances, we will have a particular type of phenomenon, the so-called Kelvin-Helmholtz (KH) instability. In this paper we will address to the basic theory of such instabilities, explaining how they arise from the hydrodynamic equations and showing the numerical simulation of a particular case. Besides, we show examples of other MHD instabilities which are usually found in astrophysical processes.